No. E-13-AAA- Reduction of computational cost for design of wind turbine tower against fatigue failure Ali R. Fathi, Hamid R. Lari, Abbas Elahi Wind turbine Technology Development Center Niroo Research Institute (NRI) Tehran, 1468617151, Iran. afathi@nri.ac.ir, hlari@nri.ac.ir, aelahi@nri.ac.ir Abstract In this paper, fatigue analysis of a steel tubular wind turbine tower is presented. This research clarifies the extent of contribution from each design load case on the total damage (aggregate of damages induced by fatigue design load cases) experienced by the tower during its life time. Contribution of the normal and shear stresses on the total damage are also distinguished. Fatigue analysis of a wind turbine tower is onerous since it requires taking the impact of many different load cases and contribution of normal and shear stresses into account. This paper singles out the most contributing load cases and stresses in fatigue analysis and therefore can be applied to reduce the relevant computational cost significantly. Keywords Wind turbine, Tubular steel tower, Fatigue analysis, Computational cost I. INTRODUCTION In the last decades, the prospect of energy shortage, environmental impacts of fossil fuels, and hazards of the nuclear energy has focused the attentions to the wind energy and use of wind turbines, among other green energy sources. Tower is one of the main components of a wind turbine that makes the high velocity winds available to the rotor by keeping the other components high above the ground. Efficient and accurate design of the tower is of high importance not only because it bears the other components, but also because it s cost usually forms a significant part of the total cost of a wind turbine [1]. Nowadays, vast majority of the commercial wind turbine towers are tubular steel towers []. One essential aspect of the wind turbine design process is designing that with respect to the fatigue strength of its components [3]. However, little attention has yet been paid to this matter in the literature. Handbooks and guidelines (e.g. [1, and 3]) suggest some brief description of the necessity and importance of the fatigue analysis. However none of them clearly introduces a systematic procedure to conduct this analysis. Lavassa, et al. [4] presented the results of their work on a 1MW wind turbine tower ending up with the fact that dynamic characteristics of the structure remain critical for the overall design of the steel tower. However, the procedure is unclear and no more results are presented in the paper. The report prepared by National Renewable Energy Laboratory ( NREL) [5] also presents the design of steel (and Hybrid steel-concrete) towers. In this report, Eurocode 3(EC3) [6] is suggested as a reference for fatigue analysis and the final results obtained by using the EC3 are compared to those obtained through application of the Equivalent Load (DEL) method (refer to [5] for mo re details about DEL method). In the mentioned report, influence of the mean stress on the total damage is not considered. Also, contribution of vertical component of the moment at the tower top to the total damage is not considered or discussed whereas taking its contribution to the total damage is necessary as discussed later in section. Yildirm, et al. [7] also adopted the method used in NREL report [5] for fatigue analysis of the wind turbine tower. The method suggested in this paper was employed in the design of WENRI 8, a MW wind turbine, which meets the requirements of Germanischer Lloyd ( GL) guideline [3]. Results obtained in this research also distinguish the share of the total damage from each load case, enabling the designer to single out the most critical load case. Refer to the appendix for nomenclature and description of symbols used in the paper. II. FATIGUE LOADS The load-time series applied to the tower and other data related to the load cases are obtained using the Fatigue, Aerodynamic, Structural and Turbulence ( FAST) code. A conventional variable-speed, variable blade-pitch-to-feather configuration is applied for WENRI8 control system. Basics of this control system are described in detail in NREL technical report [8]. In such control system, the conventional approach for controlling power-production operation relies on the design of two basic control systems: a generator-torque controller and a full-span rotor-collective blade-pitch controller. The two control systems are designed to work independently, for the most part, in the below-rated and above-rated wind-speed range, respectively [8]. Loads also are extracted in different yaw errors as suggested in GL guideline [3] (refer to section 4.3 of [3] for more information). All of the main components of a wind turbine are exposed to fatigue loading and the tower is not an exception. Load cases introduced in GL guideline [3], define the loads applied to the wind turbine in the course of its anticipated life span (
years). Table 1 shows load cases whose contributions to the total damage are mandatory to be considered as per GL guideline [3]. Table presents the recurrence of load cases during the life time of the tower and associated wind speed for each load case. Number of recurrences is obtained by the suggestions of GL [3] and Weibull wind distribution of the wind farm. Components of the applied loads on the tower are defined by the coordinate systems shown in Fig.1. Tower base coordinate system (x t, y t, z t ) is fixed in the support platform (foundation) so that it follows the translation and rotation of the platform (foundation) [9]. Tower top coordinate system ( x p, y p, z p ) is fixed to the top of the tower and translates and rotates as the tower bends or translates [9]. Internal forces and moments in arbitrary intermediate sections of the tower are allowed to be determined by linear interpolation [3]. Totally 6 loading components (3 force and 3 moment components) are applied to each tower section. For fatigue analysis of the wind turbine tower, however, consideration of the rotor thrust F x, tilting moment M y and tower torsional moment M z is sufficient [3]. Fig. shows a plot of the thrust component of the force applied to the tower top in seconds of wind turbine operation in while the yaw error is and the wind speed is 16 m/s. Highly variable loads demonstrated in Fig. show why fatigue strength consideration for the design of wind turbine tower is necessary. According to Fig., F x oscillates with a mean value of about 15- kn. The variable cyclic loadings on the tower give rise to variable cyclic stresses which likewise oscillate about a mean value. Since the mean stresses are not negligible (see Fig., section 5 and Figs. 4 to 7), their influence on the fatigue strength shall be taken into account [3, 6]. III. FATIGUE STRENGTH The fatigue strength for nominal stress ranges (refer to [6] for definition of the nominal stress) is presented by a series of (log σ)-(log N a ) curves and (log τ)-(log N a ) curves, referred to as (S-N) curves, which correspond to typical detail categories. Each detail category is designated by a number which represents (in N/mm ) the reference value σ c (or τ c ) for the fatigue strength at million stress cycles (refer to [6] for more details and descriptions). Regarding the fatigue strength, circumferential weldings on the tower shell are more critical than longitudinal weldings. Considering the circumferential weldings, detail category 71 is selected for the wind turbine tower design. Note that though detail category 8 is suggested for tower shell in some references (e.g. [1]), the detail category of the tower shell is chosen so that its detail category wouldn t fall when the interior attachments are welded to the tower (refer to [6] for more information). Fig.3 shows the S-N curve for detail category 71 for direct (normal) stress ranges in which σ D denotes fatigue limit for constant amplitude stress ranges at 5 million direct (normal) stress cycles and σ L denotes the cut-off limit (for more details refer to [6]). Stress ranges below the cut-off limit do not contribute to the total damage [6]. Concerning the wind turbine tower, direct (normal) stress is the stress in the longitudinal direction of the tower, i.e. the stress component normal to each (horizontal) tower section ( also referred to as the longitudinal stress) [1]. The number of direct (normal) stress cycles that the wind turbine tower can tolerate without fracture can be obtained through (1-a) and (1-b) [6]. N a a c 3 6 6 1 if Na 51 5 (1-a) 6 6 8 c Na 1 if 51 Na 1 (1-b) a S-N curve for the shear stress range is the same as the one for direct (normal) stress range except that m=5 up to 1 8 stress cycles, and the curve flattens thereafter (for more information refer to [6]). According to Eurocode 3, τ c =1 MPa [6, 11 and 1] for the wind turbine tower under consideration. It is worthwhile to mention here that in a wind turbine tower, shear stress ranges are usually much smaller than direct (longitudinal) stress ranges (see section 5). This reduces the dependence of total damage on the damage induced by shear stress ranges and τ c selection significantly. So designer could be not oversensitive to small errors in estimation and selection of the shear stress detail category (because the influence of the most proper selection of shear stress detail category on final result is negligible). Furthermore, making use of Eurocode 3 gives rise to a conservative design [1] and this extra safety margin can compensate the potential small impacts of the inaccuracy in τ c selection. τ L can be worked out by referring to the S-N curve for the shear stress [6]. IV. STRESS RANGE MODIFICATION Real stress ranges can be modified by multiplying a factor for the influence of mean stress denoted by F m [3]. F m can be worked out using Eq.(5-a) if p 1 or Eq.(5-b) if p>1 where p is obtained using Eqs.() to (4). p 1 (1 M ) 1 u u u () M.35.1 (3) y y 1 ar u. (4) M 1 F m 1 (1 p). a 1 p. a a (1 p) 1 p. a a (1 p) (5-a) 1 p. a 1 1 p. a F m (5-b) a (1 p) (1 p). a a (1 p) where 1 R ar a. (6) 1 R y
No. E-13-AAA- TABLE I. DESIGN LOAD CASES THAT THEIR CONTRIBUTION TO THE TOTAL DAMAGE MUST BE CONSIDERED ACCORDING TO [3] No. No Design situation No. No. Design situation 1 6 Start-up Power production 7 Normal shut-down 3 8 parked 4-1 Power production plus 5 - occurrence of fault TABLE II. WIND SPEED AND NUMBER OF THE RECURRENCES OF FATIGUE DESIGN LOAD CASES (S) IN YEARS (NUMBER OF RECURRENCES BASED ON GL SUGGESTIONS AND WEIBULL WIND DISTRIBUTION OF THE WIND FARM) Wind Speed (m/s) No. of No. of Wind Speed(m/s) Recurrence Recurrence 4 8417 5 6 135 11, 5 1-8 991 11, 5 1 1 8493 5 1 686 3 14 4 11 1 16 436 5 1 18 1367 3 75 11 1 384 5 1 4 166 3 5443 11, 5 67 34 65 11, 5 6171-1 5 11, 5 6171 z P x P y P z t x t y t (a) (b) Fig. 1 Schematic of the wind turbine tower; coordinate systems at the bottom and top of the tower (a) and the tower dimensions in mm (b)\
Fx (kn) 45 4 35 3 5 15 1 5 5 1 15 Time (sec) Fig. Fx at the tower top (Yaw Bearing) in P-Coordinate system 1 3 m=3 m=5 1 5 Fig. 3 S-N curve for direct (normal) stress ranges, detail category 71 [6]. R is the stress ratio obtained by Eq.(7): max R (7) min Finally real stress range can be modified using Eq.(8) as below. a Fm. ar (8) Here modification of the direct (normal) stress ranges is formulated. The shear stresses, also, could be treated in the same way to be modified (by substituting the parameters related to normal stress by their associated shear stress). In order to take into account the influence of mean stresses, σ a and τ a has to be considered rather than real direct and shear stress ranges ( σ ar and τ ar ) when using the corresponding S-N curve. V. PROCEDURE FOR DAMAGE CALCULATION Fatigue analysis as a stage of WENRI8 wind turbine tower design is conducted through a code developed via MATLAB. The following procedure (presented as a set of steps) is employed. 1- Sorting load-time series: Put the load-time series of relevant load cases (see Table.1) with the same number of recurrences (see Table ) in one input file. Note that in the fatigue loading calculation, each simulation run shall be performed with a different initial value for producing the turbulent wind field (see [3] section 4..3.1.). Therefore for example, there are 4 distinct input files for NTM, when (average) wind speed is 4 m/s. The input files differ from each other in yaw error magnitude and the model used for wind turbulence. All mentioned input files must be consolidated into one input file. This shall be done for all the s in Table 1. - Conversion of load-time series to stress-time series: a programming code is developed which receives the relevant load-time series (see section ) and provides stress-time series as the output. The wind turbine tower is assumed as a beam for the structural calculations. 3- Reading the generated input: Read the input files prepared in step 1 and produce the stress-time series using the programming code prepared in step. This is done by reading one distinct file at a time. 4- Application of Rain-flow algorithm: The Rain-flow algorithm is used [13] to obtain σ ar, σ m, τ ar,τ m and n. 5- Modification of stress ranges: Employ the procedure described in section 4 (Eq. (8)) to modify the real stress ranges (σ ar and τ ar ) in order to take the effect of mean stresses (σ m and τ m ) into account and obtain (σ a and τ a ). 6- Elimination of modified stress ranges with low ranges: Eliminate (consider them to be zero) the stress ranges ( σ a s, τ a s) which fall below the cut-off limit. These stress ranges do not contribute to the total damage and fatigue [6]. 7- Calculation of the number of cycles to failure: Calculate N a (number of cycles allowed for σ a or τ a without fracture) using the associated S-N curve. One is allowed, for simplification, to apply the 4
conservative assumption that the slope of the S-N curve remains equal to 3 for direct ( normal) stresses (see [3], section 5.3.3.4) for stress ranges greater than the cut-off limit. In this case one can readily use only Eq.(1-a) to evaluate N a for normal stresses. Remember that for design purposes, σ c must be reduced by an appropriate safety factor in this stage. 8- Calculation of the damage contribution caused by the read input file: The damage ( D= n Na ) for the read input file is calculated and multiplied by the number of recurrences. The resulted figure is stored as the damage attributable to the read input file. 9- Calculation of the total damage according to Miner s Rule: Miner s rule states that the aggregate of all individual damages caused by each load case, builds up the total damage ( D t ). D t must be less than 1 to make sure that the structure is safe with respect to fatigue failure [6]. Miner s rule is presented via Eq. (9): ni D t Di (9) N i ai where n i is the number of stress cycles resulted from the ith input file and N ai is the number of stress cycles that the structure can tolerate without fracture. It is obtained by referring to the relevant S-N curve. Therefore, the value obtained for damage in step 8 must be added to the aggregate of the damages caused by all previous input files. The initial value of the total damage is considered to be zero and the damage resulted from the read input file is added. Then, step 1 is repeated and the damage caused by the next input file is added. This process is followed to cover all the relevant s (see Table ). Fig.4 shows the results of rain-flow algorithm for counting direct (normal) stress cycles that a point of the tower located at the height of 7m will endure. Vertical axis shows the number of stress cycles and X and Y axes show the stress range (amplitude) and the mean stress value respectively. Fig.4 is obtained for direct (normal) stresses when turbine operates in and the wind velocity is 18 m/s. Fig.5 shows the same data for the same point but for shear stress cycles. Note that the shear stresses (both amplitude (range) and mean stress values) are nearly less than their normal (direct) counterparts by nearly an order of magnitude. Also note that the stress ranges in Figs. 4 and 5 are not modified to reflect the influence of mean stresses. Fig. 6 shows normal (direct) mean stress and stress ranges for bottom and top of the tower. Comparison between the data for these ultimate points shows that the number of stress cycles (counted through rain-flow algorithm) for the bottom of the tower is greater than the cycles that the point located at the tower top experiences. Also note that the mean stress for the point at the tower top is approximately an order of magnitude smaller than that of a point located at the bottom of the tower. Figs. 4 to 6 are examples of what one would get by applying the first four steps mentioned above. Once data like the examples presented here in Figs. 4 to 6 are obtained, one can follow the subsequent steps and obtain the total damage. VI. RESULTS AND DISCUSSION Steps suggested above are applied to 9 critical points located at 9 sections equally spaced through the 8m tower. The critical point in each section is the point which experiences the highest stress values. The critical point of the first section (located at the bottom of the tower) is denoted as point No.1. Point is the critical point of the section located at 1m above the foundation level and in the same way point No.9 is located at the tower top. The results in this section are obtained for these 9 points. Fig.8 shows the influence of mean stress on the damage caused by each in different critical points of the tower. Fig.8 also demonstrates that has the most significant effect on the total damage of all points. Fig.9 compares the damage attributable to and aggregate of the damages caused by all the s ( including ). Table.3 demonstrates the damage contributed from to the total damage caused by all the load cases. The results in this research show that the share of damage caused by shear stresses is absolutely negligible. In the case under study, all the modified shear stress ranges fall below the cut-off limit and so has no contribution to the total damage of the tower. Table.4 shows ratio of the "damage caused when the mean stress influence is not considered" to the "true total damage (which has taken the influence of mean stress into account)" for. In Table.4 D n denotes the damage caused by when mean stress influence is not considered. Figs. 8 and 9 and Table.3 clearly show that the computational cost incurred for the fatigue design of a wind turbine can be significantly reduced by considering the design load case without significant deviation from the results obtained by considering all the design load cases which are required by international standards and guidelines (e.g. GL [3]) 5
Fig. 4 Number of cycles, mean direct (normal) stress and direct (normal) stress ranges of the cycles for a point located at 7m in, wind velocity =18 m/s Fig. 5 Number of cycles, mean shear stress and shear stress ranges of the cycles for a point located at 7m in, wind velocity= 18 m/s (a) (b) Fig. 6 Number of cycles, mean shear stress and shear stress ranges of the cycles for a point located at the bottom of the tower (a) and tower top (b) in, wind velocity =8 m/s.5.5...15.1.5. 1 3 4 5 6 7 8 Tower Height.15.1.5. 1 3 4 5 6 7 8 Tower Height (a) (b) Fig. 7 Total damage induced by load cases that their damage impact must be accounted versus the tower height (in m), when "mean stress influence" is considered (a) and when "mean stress influence" is not considered (b) 6
No. E-13-AAA-..16.1.8.4..16.1.8.4-1 - -1 - (a) at the bottom of the tower (b) at 1 m...16.16.1.8.1.8.4.4-1 - -1 - (c) at m (d) at 3 m..16..16.1.8.1.8.4.4-1 - -1 - (e) at 4 m (f) at 5 m..16..16.1.8.1.8.4.4-1 - -1 - (g) at 6 m (h) at 7 m..16.1.8.4-1 - (i) at 8 m (tower top) Fig. 8 Total damage induced in different points at different heights along the tower (-8m) for points to 9
.14.1 All s (including ).1.8.6.4. 1 3 4 5 6 7 8 Tower Height (m) Fig. 9 Comparison of damage caused by and damage caused by all s TABLE III. RATIO OF THE DAMAGE INDUCED BY TO THE DAMAGE CAUSED BY ALL OTHER S Height (m) 1 3 4 5 6 7 8 caused by 1 1 (%) caused by all s 94. 93.9 94. 94.4 95.4 94.9 97.4 98.6 83. TABLE IV. RATIO OF "DAMAGE CAUSED BY WHEN MEAN STRESS INFLUENCE IS NOT CONSIDERED (DN)" TO THE "TOTAL DAMAGE" Height (m) 1 3 4 5 6 7 8 D n 1.91 1.91 1.85 1.9 1.85 1.91 1.78 1.65 1.34 Total damage VII. CONCLUSION In this paper, the procedure applied for the design of a MW wind turbine (WENRI8) was presented. Contribution of each of the load cases that are required for the fatigue analysis (according to appropriate international standards and guidelines) was determined. Contribution of the shear forces on the total damage was also determined. These results are of high importance and helpful to the wind turbine tower design process in reducing the computational cost by a significant extent. REFERENCES [1] Guidelines for design of wind turbines-dnv/riso, second edition, JydskCentralrykkeri, Denmark,. [] T. Burton, D. Sharpe, Nick Jenkins, E. Bossanyi, Wind energy handbook, John Wiley & Sons, 1. [3] Guideline for the certification of wind turbines, Germanischer Lloyd Industrial Services GmbH, 1. [4] Lavassas, G. Nilolaidis, P. Zervaz, E. Efthimiou, I.N. Doudoumis, C.C. Baniotopoulos, Analysis and design of the prototype of a steel 1-MW wind turbine tower, Engineering Structures Vol 5, pp 197-116, 3. [5] LWST Phase I project conceptual design study: Evaluation of design and construction approaches for economical hybrid steel/concrete wind turbine towers, National Renewable Energy Laboratory (NREL), 4. [6] BS EN 199-9, Design of steel structures, Part 1-9: Fatigue, 5. [7] S. Yildirm, Ibrahim Özkol, Wind turbine tower optimization under various requirements by using generic algorithm, Scientific Reaserach (http://www.scirp.org/journal/eng), 1. [8] Jonkman, J.M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine, Technical report NREL/TP-5-41958, 7. [9] FAST User s Guide, last updated on August 1 for Version 6., 5. [1] DIN 188-7, Execution and constructor s qualification, English translation, 8. [11] Gustafsson J., Saarinen J., Multi-axial fatigue in welded details-an investigation of existing design approaches, Master s Thesis in Master Degree Programme Civil Engineering, Department of Civil and Environmental Engineering, Division of Steel Structures, Chalmers University of Technology, 7. [1] Bäckstörm M., Mariques G., Interaction equations for multi-axial fatigue assessment of welded structures. Fatigue and Fracture of Engineering Materials and Structures, No.7, 4, pp. 993. [13] Nieslony, A,. Rainflow Counting Algorithm, 1. 8
No. E-13-AAA- APPENDIX Notation NOMENCLATURE Description Design Load Case σ ar Real direct (normal) stress range D σ m Mean direct (normal) stress D n caused by when mean stress influence is not considered σ y Yield stress of the material D t Total damage τ Shear stress F m Factor for influence of mean stress τ a Modified shear stress range m Slope of the fatigue strength curve τ ar Real shear stress range n Number of stress cycles τ m Mean shear stress N a Allowed number of stress cycles for a specific Fatigue direct (normal) strength for million σ stress range c stress cycles R Stress ratio τ c Fatigue shear strength for million stress cycles x p, y p, z p Tower top coordinate system σ D Fatigue limit for constant amplitude direct (normal) stress ranges at 5 million stress cycles x t, y t, z t Tower base coordinate system σ L Cut-off limit for direct (normal) stress ranges σ Direct (normal) stress τ L Cut-off limit for shear stress ranges σ a Modified direct (normal) stress range